A conversational introduction to algebraic number theory
Pollack, Paul,
A conversational introduction to algebraic number theory : arithmetic beyond Z / Paul Pollack - Providence, Rhode Island : AMS, American Mathematical Society, ©2017 - ix, 316 pages : illustrations ; 22 cm. - Student mathematical library, v. 84. .
Getting our feet wetCast of charactersQuadratic number fields: First stepsParadise lost--and foundEuclidean quadratic fieldsIdeal theory for quadratic fieldsPrime ideals in quadratic number ringsUnits in quadratic number ringsA touch of classMeasuring the failure of unique factorizationEuler's prime-producing polynomial and the criterion of Frobenius-RabinowitschInterlude: Lattice pointsBack to basics: Starting over with arbitrary number fieldsIntegral bases: From theory to practice, and backIdeal theory in general number ringsFiniteness of the class group and the arithmetic of $\overline}$Prime decomposition in general number ringsDirichlet's units theorem, IA case study: Units in $\mathbb[\sqrt[3]]$ and the Diophantine equation $X^3-2Y^3=\pm1$Dirichlet's units theorem, IIMore Minkowski magic, with a cameo appearance by HermiteDedekind's discriminant theoremThe quadratic Gauss sumIdeal density in quadratic number fieldsDirichlet's class number formulaThree miraculous appearances of quadratic class numbersIndex.
978147044890
Mathematics
Algebra
Algebraic number theory.
Number theory -- Algebraic number theory: global fields -- Algebraic number theory: global fields.
512.74 POL
A conversational introduction to algebraic number theory : arithmetic beyond Z / Paul Pollack - Providence, Rhode Island : AMS, American Mathematical Society, ©2017 - ix, 316 pages : illustrations ; 22 cm. - Student mathematical library, v. 84. .
Getting our feet wetCast of charactersQuadratic number fields: First stepsParadise lost--and foundEuclidean quadratic fieldsIdeal theory for quadratic fieldsPrime ideals in quadratic number ringsUnits in quadratic number ringsA touch of classMeasuring the failure of unique factorizationEuler's prime-producing polynomial and the criterion of Frobenius-RabinowitschInterlude: Lattice pointsBack to basics: Starting over with arbitrary number fieldsIntegral bases: From theory to practice, and backIdeal theory in general number ringsFiniteness of the class group and the arithmetic of $\overline}$Prime decomposition in general number ringsDirichlet's units theorem, IA case study: Units in $\mathbb[\sqrt[3]]$ and the Diophantine equation $X^3-2Y^3=\pm1$Dirichlet's units theorem, IIMore Minkowski magic, with a cameo appearance by HermiteDedekind's discriminant theoremThe quadratic Gauss sumIdeal density in quadratic number fieldsDirichlet's class number formulaThree miraculous appearances of quadratic class numbersIndex.
978147044890
Mathematics
Algebra
Algebraic number theory.
Number theory -- Algebraic number theory: global fields -- Algebraic number theory: global fields.
512.74 POL
